Question

Hello! Need help with this, please explain in an easy way I am in year 9

Answer 1

Let's factor the trinomial step by step:

1. Multiply and divide the whole trinomial by the leading coefficient. For the middle term, leave it expressed:

`3x^2-20x+12\rightarrow(9x^2-20(3x)+36)/(3)`

2. We'll factor just like a regular x^2+bx+c trinomial:

• Open two sets of parenthesis and put the square root of the first term on each one

`((3x)(3x))/(3)`

• Put the sign of the second term of the trinomial in the first set of parenthesis, and the result of multiplying the sign of the second term by the sign of the third term on the second set:

`((3x)(3x))/(3)\rightarrow((3x-)(3x-))/(3)`

• Find two numbers whose product is 36 and whose sum is 20

`\begin{gathered} 18\cdot2=36 \\ 18+2=20 \\ \\ \rightarrow18,2 \end{gathered}`

• Fill both sets with such numbers, in ascending order:

`((3x-)(3x-))/(3)\rightarrow((3x-18)(3x-2))/(3)`

3. Simplify one of the terms with the denominator:

`((3x-18)(3x-2))/(3)\rightarrow(3(x-6)(3x-2))/(3)\rightarrow(x-6)(3x-2)`

Therefore, the factorization of our trinomial is:

`(x-6)(3x-2)`